*Kirchhoff’s Current Law(KCL)*

*Kirchhoff’s Current Law(KCL)*

According to KCL, at any moment, the algebraic sum of flowing currents through a point in a network is Zero. In simple words, the sum of incoming currents to a point is equal to the sum of outgoing currents from that point. Remembering this much would be enough.

From figure (a): **I**_{1 }**+ I**_{5 }**= I**_{2 }**+ ****I**_{3 }**+ I**_{4}

From figure (b): **I**_{1 }**= I**_{2 }**+ ****I**_{3}_{ }i.e. 6A = 2A + 4A

The theory and understanding of KCL is really easy. The main aspect is the application of KCL which is not tough either.

**Kirchhoff’s Voltage Law(KVL)**

**Kirchhoff’s Voltage Law(KVL)**

In simplest form, it can be put up as the algebraic sum of the EMF applied in a circuit is equal to the algebraic sum of the voltage drops in the elements. This law is also known as Voltage Law or Mesh law.

KCL and KVL are used simultaneously to simplify circuits and find the missing data.

Might sound a bit confusing but let’s look at an example and things would be really easy after that.

Assume currents to flow in directions indicated by arrows.

Applying KCL on Junctions C and A, we can deduce that:

Current in mesh ABC = *i*_{1}

Current in Mesh CA = *i*_{2}

Hence, current in Mesh CDA = *i*_{1} – *i*_{2}

Now, Apply KVL on Mesh ABC, 20V is acting in clockwise direction. Equating the sum of IR products, we get;

**10***i*_{1}** + 4***i*_{2}** = 20 ……………. (1)**

**NOTE: Only R**_{1 }**, R**_{2 }**and E**_{1 }**are involved in mesh ABC.**

Also, in mesh ACD, 12 volts are acting in clockwise direction, then:

8(*i*_{1}–*i*_{2}) – 4*i*_{2}= 12

Or, **8****i**_{1}** – 12****i**_{2}** = 12 ……………. (2)**

**NOTE: Only R**_{2 }**, R**_{3 }**and E**_{2 }**are involved in mesh ACD.**

Now, we have framed two equations and that’s all we need. On solving,

i_{1 }= 1.895 A and i_{2 }= 0.263 A

Solving circuits can be made simpler and easier using different methods of circuit solving techniques. We will make short articles on those methods too.

Authored By:- Cdt. Vikramaditya Patra, TMI